On possible generalisations of quasi-contractions - CSEH, Tünde; KAJÁNTÓ, Sándor; LUKÁCS, Andor (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
This paper investigates whether some fixed point theorems for quasi-contractions on metric spaces introduced by C´iri´c in [1] and generalised by Kumam et al. in [2] can be improved further. It turns out that the answer is negative. We provide two examples of complete metric spaces and two operators without fixed points. We prove that for any possible straightforward relaxation of generalised quasi-contractive conditions, one of these operators satisfies the condition. Mathematics Subject Classification (2010): 47H10, 54H25. Received 19 May 2021; Accepted 12 April 2022.